The band limited nature of SAR data manifests itself in the form of two annoying phenomena: resolution limitation and "sidelobe" ringing, a manifestation of Gibb's phenomena. Most traditional attempts to control the former tend to exacerbate the latter. This results in the classic trade off between sidelobe energy levels and maximum resolution. Spatially variant apodization (SVA) and super-SVA represent approaches to this problem, as described in U.S. Pat. Nos. 5,349,359 and 5,686,922, both of which are incorporated herein in their entirety by reference. The SVA algorithm has been very successful in circumventing this trade off by using a spatially varying aperture function that minimizes the output energy.
In practice, at any given point in the image domain, there exists a frequency domain weighting function which corresponds to zero output energy at that given point (in fact, there exist many such weighting functions). If no constraints are imposed, the minimal output of such a spatially variant frequency domain aperture will tend to zero. In SVA, the minimization is regularized by imposing constraints on the allowed weighting functions, namely the frequency domain weighting functions are restricted to the cosine on pedestal family of functions, with the coefficient of the cosine being constrained to the range between 0 and 1. The choice of the cosine on pedestal family of functions is partially one of computational convenience; they can be efficiently on integer Nyquist sampled data by means of a three point convolver. The constraint on the coefficient of the cosine function (0.ltoreq..omega..ltoreq.1) restricts the aperture to a classic set of weighting functions that have low energy in the sidelobe regions.